Modeling the Connectome of a Simple Spinal Cord (original) (raw)
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PLoS ONE, 2014
Relating structure and function of neuronal circuits is a challenging problem. It requires demonstrating how dynamical patterns of spiking activity lead to functions like cognitive behaviour and identifying the neurons and connections that lead to appropriate activity of a circuit. We apply a ''developmental approach'' to define the connectome of a simple nervous system, where connections between neurons are not prescribed but appear as a result of neuron growth. A gradient based mathematical model of two-dimensional axon growth from rows of undifferentiated neurons is derived for the different types of neurons in the brainstem and spinal cord of young tadpoles of the frog Xenopus. Model parameters define a twodimensional CNS growth environment with three gradient cues and the specific responsiveness of the axons of each neuron type to these cues. The model is described by a nonlinear system of three difference equations; it includes a random variable, and takes specific neuron characteristics into account. Anatomical measurements are first used to position cell bodies in rows and define axon origins. Then a generalization procedure allows information on the axons of individual neurons from small anatomical datasets to be used to generate larger artificial datasets. To specify parameters in the axon growth model we use a stochastic optimization procedure, derive a cost function and find the optimal parameters for each type of neuron. Our biologically realistic model of axon growth starts from axon outgrowth from the cell body and generates multiple axons for each different neuron type with statistical properties matching those of real axons. We illustrate how the axon growth model works for neurons with axons which grow to the same and the opposite side of the CNS. We then show how, by adding a simple specification for dendrite morphology, our model ''developmental approach'' allows us to generate biologically-realistic connectomes.
Scientific Reports, 2017
During nervous system development growing axons can interact with each other, for example by adhering together in order to produce bundles (fasciculation). How does such axon-axon interaction affect the resulting axonal trajectories, and what are the possible benefits of this process in terms of network function? In this paper we study these questions by adapting an existing computational model of the development of neurons in the Xenopus tadpole spinal cord to include interactions between axons. We demonstrate that even relatively weak attraction causes bundles to appear, while if axons weakly repulse each other their trajectories diverge such that they fill the available space. We show how fasciculation can help to ensure axons grow in the correct location for proper network formation when normal growth barriers contain gaps, and use a functional spiking model to show that fasciculation allows the network to generate reliable swimming behaviour even when overall synapse counts are...
Dynamic Computational Model of the Human Spinal Cord Connectome
Neural Computation, 2018
Connectomes abound, but few for the human spinal cord. Using anatomical data in the literature, we constructed a draft connectivity map of the human spinal cord connectome, providing a template for the many calibrations of specialized behavior to be overlaid on it and the basis for an initial computational model. A thorough literature review gleaned cell types, connectivity, and connection strength indications. Where human data were not available, we selected species that have been studied. Cadaveric spinal cord measurements, cross-sectional histology images, and cytoarchitectural data regarding cell size and density served as the starting point for estimating numbers of neurons. Simulations were run using neural circuitry simulation software. The model contains the neural circuitry in all ten Rexed laminae with intralaminar, interlaminar, and intersegmental connections, as well as ascending and descending brain connections and estimated neuron counts for various cell types in every...
Neuroinformatics, 2009
We present a simulation framework, called NETMORPH, for the developmental generation of 3D large-scale neuronal networks with realistic neuron morphologies. In NETMORPH, neuronal morphogenesis is simulated from the perspective of the individual growth cone. For each growth cone in a growing axonal or dendritic tree, its actions of elongation, branching and turning are described in a stochastic, phenomenological manner. In this way, neurons with realistic axonal and dendritic morphologies, including neurite curvature, can be generated. Synapses are formed as neurons grow out and axonal and dendritic branches come in close proximity of each other. NETMORPH is a flexible tool that can be applied to a wide variety of research questions regarding morphology and connectivity. Research applications include studying the complex relationship between neuronal morphology and global patterns of synaptic connectivity. Possible future developments of NETMORPH are discussed.
Deriving physical connectivity from neuronal morphology
Biological Cybernetics, 2003
A model is presented that allows prediction of the probability for the formation of appositions between the axons and dendrites of any two neurons based only on their morphological statistics and relative separation. Statistics of axonal and dendritic morphologies of single neurons are obtained from 3D reconstructions of biocytin-filled cells, and a statistical representation of the same cell type is obtained by averaging across neurons according to the model. A simple mathematical formulation is applied to the axonal and dendritic statistical representations to yield the probability for close appositions. The model is validated by a mathematical proof and by comparison of predicted appositions made by layer 5 pyramidal neurons in the rat somatosensory cortex with real anatomical data. The model could be useful for studying microcircuit connectivity and for designing artificial neural networks.
Can Simple Rules Control Development of a Pioneer Vertebrate Neuronal Network Generating Behavior?
Journal of Neuroscience, 2014
How do the pioneer networks in the axial core of the vertebrate nervous system first develop? Fundamental to understanding any full-scale neuronal network is knowledge of the constituent neurons, their properties, synaptic interconnections, and normal activity. Our novel strategy uses basic developmental rules to generate model networks that retain individual neuron and synapse resolution and are capable of reproducing correct, whole animal responses. We apply our developmental strategy to young Xenopus tadpoles, whose brainstem and spinal cord share a core vertebrate plan, but at a tractable complexity. Following detailed anatomical and physiological measurements to complete a descriptive library of each type of spinal neuron, we build models of their axon growth controlled by simple chemical gradients and physical barriers. By adding dendrites and allowing probabilistic formation of synaptic connections, we reconstruct network connectivity among up to 2000 neurons. When the resulting "network" is populated by model neurons and synapses, with properties based on physiology, it can respond to sensory stimulation by mimicking tadpole swimming behavior. This functioning model represents the most complete reconstruction of a vertebrate neuronal network that can reproduce the complex, rhythmic behavior of a whole animal. The findings validate our novel developmental strategy for generating realistic networks with individual neuron-and synapse-level resolution. We use it to demonstrate how early functional neuronal connectivity and behavior may in life result from simple developmental "rules," which lay out a scaffold for the vertebrate CNS without specific neuron-to-neuron recognition.
The Emergent Connectome in Caenorhabditis elegans Embryogenesis
The relatively new field of connectomics provides us with a unique window into nervous systems and neuronal systems function. In the model organism Caenorhabditis elegans, this promise is even greater due to the relatively small cellular size (302 cells) of the nervous system. While the adult C. elegans connectome has been characterized, the emergence of these networks in development has yet to be established. In this paper, we approach this problem using secondary data describing the birth times of terminally-differentiated cells as they appear in the embryo and connectomics data for pharyngeal neurons in the adult hermaphrodite. By combining these two sources of data, we can better understand what an incipient connectome look like. This includes identifying at what point in embryogenesis the connectome first comes into being, observing some of the earliest connectivity patterns, and making comparisons between the formally-defined connectome and the embryogenetic interactome. An analysis is also conducted to root terminally-differentiated pharyngeal neurons in their developmental cell lineage. This analysis reveals subnetworks with different properties at 300 minutes of embryogenesis. Overall, this analysis reveals important information about the birth order of specific cells, key building blocks of global connectivity, and how these structures corresponds to various embryogenetic stages during the emergence of a connectome. INTRODUCTION Connectomics can tell us a lot about the way behavior is generated from networks of neurons such as the central nervous system or retina (Seung, 2012; Helmstaedter et.al, 2013). This pattern of connectivity is hard to understand in mammalian brains (Morgan and Lichtman, 2014), but in the nematode C. elegans, the connectomics of a 302 cell nervous system can be easily visualized and analyzed. With its relatively small size and single-cell specificity, the C. elegans connectome serves as a model for function relative to more complex nervous systems (Chatterjee and Sinha, 2007). As such, data describing C. elegans connectivity are easily available in an accessible computational format and storage repository (see Methods). The C. elegans connectome has been formally-defined as a connectivity matrix by Jarrell et.al (2012) and Varshney et.al (2011). Previous attempts at characterizing the connectome in C. elegans has focused on the static adult version. Yet we can also combine connectome data with cellular data from embryogenesis to yield a dynamic version of the connectome as it emerges from developmental cells.
neuroConstruct: A Tool for Modeling Networks of Neurons in 3D Space
Neuron, 2007
Conductance-based neuronal network models can help us understand how synaptic and cellular mechanisms underlie brain function. However, these complex models are difficult to develop and are inaccessible to most neuroscientists. Moreover, even the most biologically realistic network models disregard many 3D anatomical features of the brain. Here, we describe a new software application, neuroConstruct, that facilitates the creation, visualization, and analysis of networks of multicompartmental neurons in 3D space. A graphical user interface allows model generation and modification without programming. Models within neuroConstruct are based on new simulator-independent NeuroML standards, allowing automatic generation of code for NEURON or GENESIS simulators. neuroConstruct was tested by reproducing published models and its simulator independence verified by comparing the same model on two simulators. We show how more anatomically realistic network models can be created and their properties compared with experimental measurements by extending a published 1D cerebellar granule cell layer model to 3D.
A theoretical model of neural maturation in the developing spinal cord
Cellular differentiation is a tightly regulated process under the control of intricate signaling and transcription factors networks working in coordination. Due to their complexity, these networks are studied and modelled independently despite their codependence: signals instruct transcription factors to drive cellular responses, and transcription factors provide the context for the cells to respond to signals. These reciprocal interactions make the systems dynamic, robust and stable but also difficult to dissect. Differential equation based mathematical models provide an important theoretical tool to understand the behavior of these intricate networks. In the spinal cord, recent work has shown that a network of FGF, Wnt and Retinoic Acid (RA) signaling factors regulate neural maturation by directing the activity of a transcription factor network that contains CDX at its core. Here we have used differential equation based models to understand the spatiotemporal dynamics of the FGF/W...